Densities of WDs (between \(10^4\)  g cm\(^{-3}\)  and \(10^7\)  g cm\(^{-3}\) ) causes the very high Fermi temperature (\(10^9-10^{11}\)  K). This temperature is a few orders of magnitude larger than the interior of a WD (\(\lesssim 9\times 10^7\)  K [1]}).
For this reason, we treat electrons as a gas at zero temperature. If we focus on the bosonic component, then for a WD density of the order of \(10^6\)  g cm\(^{-3}\)  the critical temperature for Bose-Einstein condensation is \(10^5\) K for the \(^4\) He component (neglecting interactions). The assumption that most of the bosonic component is condensed is very plausible.
In this paper, for simplicity, we consider bosonic component of a white dwarf as a gas at zero temperature.
However, let us mention that the description of bosons including thermal fraction is already well known [2]}.
The possibility of formation of the Bose-Einstein condensation in helium white dwarf stars was already discussed in [3]}, [4]}, [5]}, [6]}. It was argued that, indeed, in the interior of the dwarf the charged \(^4\) He nuclei are in the state of Bose-Einstein condensate whereas the relativistic degenerate electrons form a neutralizing liquid.
